represents single-variable polynomials over arbitrary rings More...

#include <polynomi.h>

Inheritance diagram for PolynomialOver< T >:

Classes
class	DivideByZero
	division by zero exception More...

class	RandomizationParameter
	specify the distribution for randomization functions More...

ENUMS, EXCEPTIONS, and TYPEDEFS
typedef T	Ring

typedef T::Element	CoefficientType

INPUT/OUTPUT
std::istream &	Input (std::istream &in, const Ring &ring)

std::ostream &	Output (std::ostream &out, const Ring &ring) const

CREATORS
	PolynomialOver ()
	creates the zero polynomial

	PolynomialOver (const Ring &ring, unsigned int count)

	PolynomialOver (const PolynomialOver< Ring > &t)
	copy constructor

	PolynomialOver (const CoefficientType &element)
	construct constant polynomial

template<typename Iterator >
	PolynomialOver (Iterator begin, Iterator end)
	construct polynomial with specified coefficients, starting from coefficient of x^0

	PolynomialOver (const char *str, const Ring &ring)
	convert from string

	PolynomialOver (const byte *encodedPolynomialOver, unsigned int byteCount)
	convert from big-endian byte array

	PolynomialOver (const byte *BEREncodedPolynomialOver)
	convert from Basic Encoding Rules encoded byte array

	PolynomialOver (BufferedTransformation &bt)
	convert from BER encoded byte array stored in a BufferedTransformation object

	PolynomialOver (RandomNumberGenerator &rng, const RandomizationParameter &parameter, const Ring &ring)
	create a random PolynomialOver<T>

ACCESSORS
int	Degree (const Ring &ring) const
	the zero polynomial will return a degree of -1

unsigned int	CoefficientCount (const Ring &ring) const

CoefficientType	GetCoefficient (unsigned int i, const Ring &ring) const
	return coefficient for x^i

MANIPULATORS
PolynomialOver< Ring > &	operator= (const PolynomialOver< Ring > &t)

void	Randomize (RandomNumberGenerator &rng, const RandomizationParameter &parameter, const Ring &ring)

void	SetCoefficient (unsigned int i, const CoefficientType &value, const Ring &ring)
	set the coefficient for x^i to value

void	Negate (const Ring &ring)

void	swap (PolynomialOver< Ring > &t)

BASIC ARITHMETIC ON POLYNOMIALS
bool	Equals (const PolynomialOver< Ring > &t, const Ring &ring) const

bool	IsZero (const Ring &ring) const

PolynomialOver< Ring >	Plus (const PolynomialOver< Ring > &t, const Ring &ring) const

PolynomialOver< Ring >	Minus (const PolynomialOver< Ring > &t, const Ring &ring) const

PolynomialOver< Ring >	Inverse (const Ring &ring) const

PolynomialOver< Ring >	Times (const PolynomialOver< Ring > &t, const Ring &ring) const

PolynomialOver< Ring >	DividedBy (const PolynomialOver< Ring > &t, const Ring &ring) const

PolynomialOver< Ring >	Modulo (const PolynomialOver< Ring > &t, const Ring &ring) const

PolynomialOver< Ring >	MultiplicativeInverse (const Ring &ring) const

bool	IsUnit (const Ring &ring) const

PolynomialOver< Ring > &	Accumulate (const PolynomialOver< Ring > &t, const Ring &ring)

PolynomialOver< Ring > &	Reduce (const PolynomialOver< Ring > &t, const Ring &ring)

PolynomialOver< Ring >	Doubled (const Ring &ring) const

PolynomialOver< Ring >	Squared (const Ring &ring) const

CoefficientType	EvaluateAt (const CoefficientType &x, const Ring &ring) const

PolynomialOver< Ring > &	ShiftLeft (unsigned int n, const Ring &ring)

PolynomialOver< Ring > &	ShiftRight (unsigned int n, const Ring &ring)

static void	Divide (PolynomialOver< Ring > &r, PolynomialOver< Ring > &q, const PolynomialOver< Ring > &a, const PolynomialOver< Ring > &d, const Ring &ring)
	calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d)

Detailed Description

template<class T>
class PolynomialOver< T >

represents single-variable polynomials over arbitrary rings

Definition at line 21 of file polynomi.h.

Member Typedef Documentation

◆ Ring

template<class T >

typedef T PolynomialOver< T >::Ring

Definition at line 46 of file polynomi.h.

◆ CoefficientType

template<class T >

typedef T::Element PolynomialOver< T >::CoefficientType

Definition at line 47 of file polynomi.h.

Constructor & Destructor Documentation

◆ PolynomialOver() [1/7]

template<class T >

PolynomialOver< T >::PolynomialOver ( )

inline

creates the zero polynomial

Definition at line 53 of file polynomi.h.

◆ PolynomialOver() [2/7]

template<class T >

PolynomialOver< T >::PolynomialOver	(	const Ring &	ring,
		unsigned int	count )

inline

Definition at line 56 of file polynomi.h.

◆ PolynomialOver() [3/7]

template<class T >

PolynomialOver< T >::PolynomialOver ( const PolynomialOver< Ring > & t )

inline

copy constructor

Definition at line 60 of file polynomi.h.

◆ PolynomialOver() [4/7]

template<class T >

PolynomialOver< T >::PolynomialOver ( const CoefficientType & element )

inline

construct constant polynomial

Definition at line 64 of file polynomi.h.

◆ PolynomialOver() [5/7]

template<class T >

template<typename Iterator >

PolynomialOver< T >::PolynomialOver	(	Iterator	begin,
		Iterator	end )

inline

construct polynomial with specified coefficients, starting from coefficient of x^0

Definition at line 68 of file polynomi.h.

◆ PolynomialOver() [6/7]

template<class T >

PolynomialOver< T >::PolynomialOver	(	const char *	str,
		const Ring &	ring )

inline

convert from string

Definition at line 72 of file polynomi.h.

◆ PolynomialOver() [7/7]

template<class T >

PolynomialOver< T >::PolynomialOver	(	RandomNumberGenerator &	rng,
		const RandomizationParameter &	parameter,
		const Ring &	ring )

inline

create a random PolynomialOver<T>

Definition at line 84 of file polynomi.h.

Member Function Documentation

◆ Degree()

template<class T >

int PolynomialOver< T >::Degree ( const Ring & ring ) const

inline

the zero polynomial will return a degree of -1

Definition at line 91 of file polynomi.h.

◆ CoefficientCount()

template<class T >

unsigned int PolynomialOver< T >::CoefficientCount ( const Ring & ring ) const

Definition at line 76 of file polynomi.cpp.

◆ GetCoefficient()

template<class T >

PolynomialOver< T >::CoefficientType PolynomialOver< T >::GetCoefficient	(	unsigned int	i,
		const Ring &	ring ) const

return coefficient for x^i

Definition at line 86 of file polynomi.cpp.

◆ operator=()

template<class T >

PolynomialOver< T > & PolynomialOver< T >::operator= ( const PolynomialOver< Ring > & t )

Definition at line 92 of file polynomi.cpp.

◆ Randomize()

template<class T >

void PolynomialOver< T >::Randomize	(	RandomNumberGenerator &	rng,
		const RandomizationParameter &	parameter,
		const Ring &	ring )

Definition at line 16 of file polynomi.cpp.

◆ SetCoefficient()

template<class T >

void PolynomialOver< T >::SetCoefficient	(	unsigned int	i,
		const CoefficientType &	value,
		const Ring &	ring )

set the coefficient for x^i to value

Definition at line 182 of file polynomi.cpp.

◆ Negate()

template<class T >

void PolynomialOver< T >::Negate ( const Ring & ring )

Definition at line 190 of file polynomi.cpp.

◆ swap()

template<class T >

void PolynomialOver< T >::swap ( PolynomialOver< Ring > & t )

Definition at line 198 of file polynomi.cpp.

◆ Equals()

template<class T >

bool PolynomialOver< T >::Equals	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 204 of file polynomi.cpp.

◆ IsZero()

template<class T >

bool PolynomialOver< T >::IsZero ( const Ring & ring ) const

inline

Definition at line 120 of file polynomi.h.

◆ Plus()

template<class T >

PolynomialOver< T > PolynomialOver< T >::Plus	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 219 of file polynomi.cpp.

◆ Minus()

template<class T >

PolynomialOver< T > PolynomialOver< T >::Minus	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 250 of file polynomi.cpp.

◆ Inverse()

template<class T >

PolynomialOver< T > PolynomialOver< T >::Inverse ( const Ring & ring ) const

Definition at line 281 of file polynomi.cpp.

◆ Times()

template<class T >

PolynomialOver< T > PolynomialOver< T >::Times	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 293 of file polynomi.cpp.

◆ DividedBy()

template<class T >

PolynomialOver< T > PolynomialOver< T >::DividedBy	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 309 of file polynomi.cpp.

◆ Modulo()

template<class T >

PolynomialOver< T > PolynomialOver< T >::Modulo	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring ) const

Definition at line 317 of file polynomi.cpp.

◆ MultiplicativeInverse()

template<class T >

PolynomialOver< T > PolynomialOver< T >::MultiplicativeInverse ( const Ring & ring ) const

Definition at line 325 of file polynomi.cpp.

◆ IsUnit()

template<class T >

bool PolynomialOver< T >::IsUnit ( const Ring & ring ) const

Definition at line 331 of file polynomi.cpp.

◆ Accumulate()

template<class T >

PolynomialOver< T > & PolynomialOver< T >::Accumulate	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring )

Definition at line 104 of file polynomi.cpp.

◆ Reduce()

template<class T >

PolynomialOver< T > & PolynomialOver< T >::Reduce	(	const PolynomialOver< Ring > &	t,
		const Ring &	ring )

Definition at line 118 of file polynomi.cpp.

◆ Doubled()

template<class T >

PolynomialOver< Ring > PolynomialOver< T >::Doubled ( const Ring & ring ) const

inline

Definition at line 136 of file polynomi.h.

◆ Squared()

template<class T >

PolynomialOver< Ring > PolynomialOver< T >::Squared ( const Ring & ring ) const

inline

Definition at line 138 of file polynomi.h.

◆ EvaluateAt()

template<class T >

PolynomialOver< T >::CoefficientType PolynomialOver< T >::EvaluateAt	(	const CoefficientType &	x,
		const Ring &	ring ) const

Definition at line 132 of file polynomi.cpp.

◆ ShiftLeft()

template<class T >

PolynomialOver< T > & PolynomialOver< T >::ShiftLeft	(	unsigned int	n,
		const Ring &	ring )

Definition at line 149 of file polynomi.cpp.

◆ ShiftRight()

template<class T >

PolynomialOver< T > & PolynomialOver< T >::ShiftRight	(	unsigned int	n,
		const Ring &	ring )

Definition at line 167 of file polynomi.cpp.

◆ Divide()

template<class T >

void PolynomialOver< T >::Divide	(	PolynomialOver< Ring > &	r,
		PolynomialOver< Ring > &	q,
		const PolynomialOver< Ring > &	a,
		const PolynomialOver< Ring > &	d,
		const Ring &	ring )

static

calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d)

Definition at line 430 of file polynomi.cpp.

◆ Input()

template<class T >

std::istream & PolynomialOver< T >::Input	(	std::istream &	in,
		const Ring &	ring )

Definition at line 337 of file polynomi.cpp.

◆ Output()

template<class T >

std::ostream & PolynomialOver< T >::Output	(	std::ostream &	out,
		const Ring &	ring ) const

Definition at line 370 of file polynomi.cpp.

The documentation for this class was generated from the following files:

Classes

ENUMS, EXCEPTIONS, and TYPEDEFS

INPUT/OUTPUT

CREATORS

ACCESSORS

MANIPULATORS

BASIC ARITHMETIC ON POLYNOMIALS

Detailed Description

Member Typedef Documentation

◆ Ring

◆ CoefficientType

Constructor & Destructor Documentation

◆ PolynomialOver() [1/7]

◆ PolynomialOver() [2/7]

◆ PolynomialOver() [3/7]

◆ PolynomialOver() [4/7]

◆ PolynomialOver() [5/7]

◆ PolynomialOver() [6/7]

◆ PolynomialOver() [7/7]

Member Function Documentation

◆ Degree()

◆ CoefficientCount()

◆ GetCoefficient()

◆ operator=()

◆ Randomize()

◆ SetCoefficient()

◆ Negate()

◆ swap()

◆ Equals()

◆ IsZero()

◆ Plus()

◆ Minus()

◆ Inverse()

◆ Times()

◆ DividedBy()

◆ Modulo()

◆ MultiplicativeInverse()

◆ IsUnit()

◆ Accumulate()

◆ Reduce()

◆ Doubled()

◆ Squared()

◆ EvaluateAt()

◆ ShiftLeft()

◆ ShiftRight()

◆ Divide()

◆ Input()

◆ Output()